Many rabbits are territorial of their cage. My boys have been neutered for over a year, and if I stick my hand in there to clean while theyre in there, theyll try to push me away. Theyll nudge with their heads and make little huffy noises while using their little front feet to push me out. I dont get nipped or bitten, but they do make it clear they dont like me cleaning.

Theyve also been pretty recently neutered. For a month or two after their neuters, they can go through hormonal phases where their hormones spike causing them to act like mean little buggers for a day or few.

I would recommend only cleaning the cage when they are not around. You can keep feeding them while theyre in the cage, so they associate you in their cage with positive things.

I don’t know how to deal with it since I’ve only every had larger animals. Horses taught me that you stand your ground and DO NOT back down or else they learn to keep doing it. I don’t know if it’s the same with rabbits. I just want to know how to handle this without damaging the relationship.

I believe it is the same with rabbits.
The fact that he successfully warned the cat off could have reinforced for him that aggression works.
So I would stand my ground with him if you’re faced with aggression, until he learns it won’t achieve anything and that you are not a threat. By that, I don’t mean baiting him into the behaviour over and over. Especially if it is fear-based because he is wary of the cat.
We do have to be respectful of their “safe space” also, so- as Mikey suggested- try to mainly attend to the cage while they are out of it. But for those times where it can’t be avoided, maybe put on protective gloves if he does try bite and try not react to the aggressiveness.